Likelihood Analysis of Large-Scale Flows

Abstract

We apply a likelihood analysis to the data of \markcite{Lauer \& Postman 1994} With $P(k)$ parametrized by $({\sigma }_8,\Gamma )$, the likelihood function peaks at ${\sigma }_8\simeq 0.3$, $\Gamma \lesssim 0.025$, indicating at face value very strong large-scale power, though at a level incompatible with COBE\@. There is, however, a ridge of likelihood such that more conventional power spectra do not seem strongly disfavored. The likelihood calculated using as data only the components of the bulk flow solution peaks at higher ${\sigma }_8$, in agreement with other analyses, but is rather broad. The likelihood incorporating both bulk flow and shear gives a different picture. The components of the shear are all low, and this pulls the peak to lower amplitudes as a compromise. The Lauer \& Postman velocity data alone are therefore {\em consistent}\/ with models with very strong large scale power which generates a large bulk flow, but the small shear (which also probes fairly large scales) requires that the power would have to be at {\em very}\/ large scales, which is strongly disfavored by COBE\@. The velocity data also seem compatible with more conventional $P(k)$ with $0.2\lesssim \Gamma \lesssim 0.5$, and the likelihood is peaked around ${\sigma }_8\sim 1$, in which case the bulk flow is a moderate, but not extreme, statistical fluctuation. Applying the same techniques to the data of \markcite{Riess, Press, \& Kirshner 1995}, the results are quite different. The flow is not inconsistent with the microwave dipole and we derive only an upper limit to the amplitude of the power spectrum: ${\sigma }_8\lesssim 1.5$ at roughly 99\%.

uuencoded, gzipped postscript. Considerable changes in details of the analysis; conclusions largely unchanged. Also available at file://ftp.cita.utoronto.ca/cita/jaffe/papers/vlet.ps.gz To be published in Ap.J., December 10, 1995

Cited by in corpus (39)

• Cosmic Flows on 100 Mpc/h Scales: Standardized Minimum Variance Bulk Flow, Shear and Octupole Moments
• Local Gravity versus Local Velocity: Solutions for $\beta$ and nonlinear bias
• A Large-Scale Bulk Flow of Galaxy Clusters
• The cosmological bulk flow: consistency with $\Lambda$CDM and $z\approx 0$ constraints on ${\sigma }_8$ and $\gamma$
• The 6dF Galaxy Velocity Survey: Cosmological constraints from the velocity power spectrum
• Are peculiar velocity surveys competitive as a cosmological probe?
• 2MTF VI. Measuring the velocity power spectrum
• The Dipole Repeller
• The Redshift Space Momentum Power Spectrum II: measuring the growth rate from the combined 2MTF and 6dFGSv surveys
• Large Scale Power Spectrum from Peculiar Velocities Via Likelihood Analysis
• Cosmic bulk flows on 50 {h}^{-1}Mpc scales: A Bayesian hyper-parameter method and multishells likelihood analysis
• Improving constraints on the growth rate of structure by modelling the density-velocity cross-correlation in the 6dF Galaxy Survey
• Bayesian 3d velocity field reconstruction with VIRBIuS
• The Far Field Hubble Constant
• Large-Scale Power Spectrum and Cosmological Parameters from SFI Peculiar Velocities
• Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA
• Large-Scale Power Spectrum and Structures From the ENEAR galaxy Peculiar Velocity Catalog
• Power Spectrum Estimation from Peculiar Velocity Catalogues
• Interpreting New Data on Large Scale Bulk Flows
• Power Spectrum Shape from Peculiar Velocity Data
• The Environmental Dependence of Brightest Cluster Galaxies: Implications for Large-Scale Flows
• A Slight Excess of Large Scale Power from Moments of the Peculiar Velocity Field
• Bulk flow and shear in the local Universe: 2MTF and COSMICFLOWS-3
• Peculiar velocities into the next generation: cosmological parameters from the SFI++ survey
• Easily Interpretable Bulk Flows: Continuing Tension with the Standard Cosmological Model
• Testing the minimum variance method for estimating large-scale velocity moments
• Exploring the Redshift-Space Peculiar Velocity Field and its Power Spectrum
• Cosmic Flow Measurement and Mock Sampling Algorithm of Cosmicflows-4 Tully-Fisher Catalogue
• Reconstructing dark matter distribution with peculiar velocities: Bayesian forward modelling with corrections for inhomogeneous Malmquist bias
• Determining the motion of the solar system relative to the cosmic microwave background using type Ia supernovae
• The Peculiar Velocity Correlation Function
• Optimal Moments for the Analysis of Peculiar Velocity Surveys
• A New Approach to Probing Large Scale Power with Peculiar Velocities
• Gaussianization of peculiar velocities and bulk flow measurement
• Testing Bayesian reconstruction methods from peculiar velocities
• Goodness-of-fit analysis of the Cosmicflows-2 database of velocities
• A probabilistic framework for cosmological inference of peculiar velocities
• Improved Methods for Estimating Peculiar Velocity Correlation Functions Using Volume Weighting
• Testing Cold Dark Matter Models Using Hubble Flow Variations